Question

Complete the input-output table for the function f(x) = (x−2)2+3 Desmos Calculator (click here) (2 points) x f(x) 1 f(1)= 4 f(4)=

Answer 1

To complete the input-output table for the function \( f(x) = (x-2)^2 + 3 \), we need to calculate the value of \( f(4) \).

1. Calculate \( f(1) \):
\[
f(1) = (1-2)^2 + 3 = (-1)^2 + 3 = 1 + 3 = 4
\]

2. Calculate \( f(4) \):
\[
f(4) = (4-2)^2 + 3 = (2)^2 + 3 = 4 + 3 = 7
\]

Now we can fill out the input-output table:

\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
1 & 4 \\
4 & 7 \\
\hline
\end{array}
\]

So, the completed input-output table shows:
- \( f(1) = 4 \)
- \( f(4) = 7 \)